Factor the following expression: $75x^2 - 27$
Answer: We can start by factoring a ${3}$ out of each term: $ {3}({25x^2} - {9})$ The second term is of the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as ${3}({a} + {b}) ({a} - {b})$ What are the values of $a$ and $b$ $ a = \sqrt{25x^2} = 5x$ $ b = \sqrt{9} = 3$ Use the values we found for $a$ and $b$ to complete the factored expression, ${3}({a} + {b}) ({a} - {b})$ So we can factor the expression as: ${3}({5x} + {3}) ({5x} - {3})$